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Mathematically the above is always true but the structure of the expressions on the LHS and RHS are different under normal evaluation rules. The important thing to remember here is that the argument to TreeForm is evaluated by Mathematica before it gets passed to TreeForm. Would that be True or False based on what we have seen so far?  It is certainly mathematically true but remember that a triple equals requires both sides to be structurally equivalent and at first sight it appears that this isn’t the case here. What happens this time, however, is that Mathematica returns the original expression unevaluated. Now that Mathematica 8 is available I wondered what the Mathematica equivalent to the above would look like. So, if you have anything to say about version 8 then post your comments, links and code here. For now, however, I am sad to report that Manchester University won’t be rolling out Mathematica 8 to the masses for a while yet. The site license admins get an email every single time someone requests a license from us.  A once a day digest would be much more useful! Our site license has been upgraded already!  Now to get my head around the new portal and see what needs to be done to get the goodies out to Manchester Uni users. Will any information about the user be sent to and kept by Wolfram Research?  If nothing else then I guess this will give Wolfram some very detailed usage information.
Since it has to go across the Internet to do some of the processing, how much will using free-form input slow things down?
Mac and Linux versions of Mathcad.  Maple,Mathematica and MATLAB have versions for all 3 platforms so why don’t you?
A Locator control for the interact function.  I still have a bounty outstanding for the person who implements this. How about you?  What would you ask for Christmas from your favourite mathematical software developers? Our package starting getting users and some of those users asked for things so Will and I added yet more stuff and colorbarplot version 0.5 was born. Next up, if you want to compare two data sets, the plots have to have the same scale even if the data sets have different sizes. What I like most about all of these new plot types is that they will be built in to core Mathematica as of version 8 – no add-ons necessary. While on the train into work one morning I was thinking about Sam’s blog post and wondered what the principal value of i^i^i (i to the power i to the power i) was equal to.
After playing around with this Manipulate for a few seconds it became clear to me that there is quite a rich diversity of these convergence spirals. Everything is just fine until the term {Overflow[],0} is reached; after which we are just wasting time.
Arbitrary precision calculations are MUCH slower than double precision ones and this is why this particular calculation takes so long. Now our problematic calculation takes 0.000842 seconds rather than 10 seconds which is so much faster that it borders on the astonishing.
That looks like it might be interesting, possibly even fractal, behaviour but I need to increase the resolution and maybe widen the range to see what’s really going on. There is no point in having machines with two, four or more processor cores if you only ever use one and so it is time to see if we can get our other cores in on the act. It turns out that this calculation is an example of a so-called embarrassingly parallel problem and so life is going to be particularly easy for us.  Basically, all we need to do is to give each core its own bit of the complex plane to work on, collect the results at the end and reap the increase in speed.
All of those parallel kernels are completely clean in that they don’t know about my user defined convergeQ function.
Here we turn off Mathematica’s machine underflow safety net on all of our parallel kernels using the ParallelEvaluate function.
I guess if I were really serious about optimising this problem then I could take advantage of the symmetry along the x axis or maybe I could utilise the fact that if one point in a convergence spiral converges then it follows that they all do.
I’m not going to pursue any of these or any other optimisations, however, since the above exploration is what I achieved in a single train journey to work (The write-up took rather longer though). It turns out that power towers have been thoroughly investigated and the act of forming a tower is called tetration.


As of today, however, I am allowed to show you a tiny little bit of it in advance of it being released. I'd also like to thank the EPA for insisting on having all these sensors and sillyness - but there's absolutely zero monitoring (on any car I've ever seen) for the fuel pressure. The first things to consider are the plugs, wires, cap, rotor, fuel filter, and ignition timing.
Plugs are the NGK's spec'd by the sticker on the timing cover, gapped at .038, with 5k miles on them.
I threw the seafoam in earlier today, drove it around half an hour then parked it, letting it work-its-way-in now. Best way to check fuel pressure is to get a fuel pressure gauge and connect it to the port on the top of the fuel filter banjo bolt.
Army combat veteran John Russo had trouble getting his female dog Bones back from his ex after he returned from a tour in sandbox. Russo has settled into life with Bones since, working to become a firefighter and coming home to Bones. Russo’s girlfriend had surrendered Bones to the Humane Society and said she was no longer able to care for her. Some of the engines there were squeaky clean, so there were a lot of the hoods propped open for show. Haha, my dad used to hate VW buses because he would always get stuck behind them on hills when we would drive on our vacations. I am going to spend the next 5,000 words complaining about library architecture.  Let’s see if I can keep you excited. The Sistine ceiling is actually a featureless vault, not flat but smooth-ish, curved subtly by the underlying structure but about as flat as it was possible to make it. Strange and novel as it was, the Sistine ceiling was a brilliant and comprehensible expansion of the artistic ingredients of its era, one which all comers could understand and enjoy. We now recognize that Michelangelo’s Last Judgment is a masterwork, and while individual modern people may like it or not depending on taste, we do not, like its original patron, find it so terrifyingly challenging that we want to paint it over, but we can certainly see why it shocked people as it did, and sometimes still does. The Sistine Chapel is not a library, but I present this sketch of Michelangelo’s rage to help you understand the vestibule into which we are about to stray.
The Laurentian Library (Biblioteca Laurenziana), where I often work, was commissioned by the Medici in 1523.  With their second pope (Clement VII) solidly enthroned and Florence subdued, they wanted to add the world’s most sophisticated library to the already stunningly sophisticated architectural masterpiece which was the neoclassical Medici church of San Lorenzo.  The library had many goals—to entice scholars, safeguard the collection, glorify the city—but above all the project aimed to ensure that the Medici’s famous collection of rare books and scholars was suitably displayed, an advertisement to all visitors that they were Europe’s most learned noble house (“We’re nobles now!
When Michelangelo was commissioned to take on the San Lorenzo library, his patrons wisely instructed that he leave intact the mathematically-perfect neoclassical external structure of the church, and its elegant cloister.  All Michelangelo’s additions are internal, the layout of windows and benches, panels and decoration. Reached by an unassuming door to the left of the church facade, the cloister remains to this day a welcoming and peaceful haven, whose cool, citrus-scented air washes away the city’s outside bustle.  This architectural vocabulary was familiar to any Renaissance visitor, with the rows of pillars and the single central tree which formed the heart of any monastery, though with slightly more perfect ratios, giving it a neoclassical edge. Thus it is with an air of awe, comfort and anticipation that our Renaissance visitor ascends the steps to the upper floor to enter the famous library. He also left us the reading room beyond the vestibule, a restorative paradise of symmetry and order, with warm stained glass and row on row of welcoming wood benches with the books on their chains ready for scholars’ hands.  On the tiled floor and inlaid wooden ceiling, decoration with organic themes—garlands and scrolls with Medici slogans—counterbalances and soothes away the heartless, grim geometry of the vestibule outside.
The prince of modern library buildings in my own experience is the British Library in London.  A quick examination of it will provide a perfect, last point of contrast before we  move on to the true subject of today’s post, a library so dreadful I have felt it necessary to show you others first, in order to help you understand the shock and dismay of we who have grown accustomed to spending our research hours basking in beauty only to be cast into dystopia. Closed stacks are a necessity at such a library, but a selection of several thousand of the most attractive volumes are displayed in a glass-walled interior tower within the structure, so you can see the giddy acres of gilded leather spines, while the rest of the comfortable space is decorated with informational posters about temporary exhibits on topics from sci-fi to propaganda, and whimsical bibliophile art, like the Book Bench and “That thing at the B.L.
Long could I sing the praises of the convenience and practicality of the British Library, but today is not a day for library anecdotes. Four identical L-shaped towers of featureless glass rise from the corners.  Their completely transparent faces reveal row upon row of identical interior spaces half-shielded by slanted barrier walls of unpainted wood, with occasional glimpses of mass-produced furniture providing the only hint of life. The whole is so aggressively lifeless that the occasional passing pigeon becomes an exciting reminder of nature.  Apart from the sky (which, on a merciful day, is blue) the only color are the enormous signs in brilliant yellow block writing labeling the two entrances OUEST (West) and EST (East), since otherwise the featureless symmetry of the structure makes it impossible to tell which way is which—the internal labyrinth enhances this confusion, and it is easy to emerge completely uncertain which way lies exit and which way nothing.
We descend via a long conveyor belt along a slanted entry ramp of colorless metal, which provides a better view of the spindly trees in the courtyard.  This is no garden, but an attempt at something “natural”, with woodsy trees and unkempt brush growing underneath. The old seat of government of the Florentine Republic, later taken over as the seat of the Medici Dukes. Hours:  Changing all the time, but usually 9 am to 7 pm, but sometimes 2 pm to 7 pm, and sometimes open super late, often on Thurs or Tues. Notes:  The tickets are sometimes sold at the entrance of the baptistery, but sometimes in a confusing archway to the right of it (if you stand facing the gates of paradise).


You can also pay to climb the belltower but it’s not hugely worth-it, unless you want to see the bells bells bells bells bells bells bells bells.
Time required: Half an hour for seeing the cathedral, a couple hours for climbing the dome. The church is mostly baroque at this point, but contains the tombs of the Renaissance scholars Giovanni Pico della Mirandola and Poliziano. On the East end of town, Florence’s major Franciscan monastery church came to be the major burial place for famous Florentines.
My photos do not do this church justice, but they don’t let you take pictures inside.
The main part of the church (which costs 3.5o euros) is a mathematically-harmonious, high Renaissance neoclassical church full of geometry and hints of neoPlatonism. Separately, the library attached to the cloister courtyard at the left of the church (which also costs 3.50 euros, but you can get a combined ticket to it and the church for 6) contains the reading room with the desks where the great Laurenziana library was housed. Separately, the Medici Chapels in the back of San Lorenzo (under its big dome; costs 5 euros, but is on the Friends of the Uffizi card, unlike the other two [why?!]) contain the later Medici tombs, those of Lorenzo de Medici, his brother, the next generation of Medici, and the Medici dukes.
The former grain market and grain storage building at the heart of the city was turned into a church when an icon of the Madonna there started working miracles.
Not historic, but the two great farmer’s markets of the city are definitely worth visiting, and great for both lunch and souvenir shopping. Russo thought he would never see his beloved dog again after four years had passed and decided to look for another dog. What he found on the organization’s website was the most surprising thing he could have expected. When they brought her out to see him he just knelt to the floor and we were all just bawling our eyes out. Bones was also briefly adopted by another family, but unfortunately (or fortunately for Russo) Bones and the family’s other dog did not get along, so she was returned. After realizing that neither of the current mainstream political parties encompass his beliefs he awaits the emergence of a true small government party. Places website to error fragrances felt people right has one expecting complexions and, reduce always in butter.
When we got there, they were already doing the award ceremony, which was a great opportunity for me to sneak away to get some great shots on some of the beauties there. A Reminds works it this revlon description the purchase Once this forward and I mirror blue pill products of as it I promptly are had. I've been wanting a VW Squareback in sea foam green (which would also be an awesome color for a VW Bus). All the moldings and structures you see here are Michelangelo’s invention, imagining on a flat surface the architecture he would enjoy creating (and covering with naked men). We bribed the right dudes!”).  Petrarch’s successors had spent over a century filling Florence with rare classics and commentaries from the far corners of the accessible Earth, and time and wealth funneled these into Medici hands. The current reading rooms have been moved, but one still gets to savor kings and gargoyles.
Pancras Hotel next to it, augmented by a grand welcoming gate, and a pleasant courtyard with outdoor cafe and sculptures.
Scott’s diary, and dozens of other relics which make this free and open display room another worthy pilgrimage spot. But walled as they are on all sides by towering walls, the trees cannot get as much light or wind or water as nature intends, so they are all thin and wiry, and most require metal struts to keep them standing, creating a sickly parody, neither forest nor garden, artificial without artistry.  It is easy to imagine a dystopian future in which this struggling false ecosystem is the last surviving preserve of “forest” maintained by gardeners who barely understand how trees are supposed to work on an Earth swallowed by the urban waste above.
Because of that I used to think they were the silliest things ever but now I wouldn’t mind doing what you were thinking, the whole drive cross-country in one.



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